RL unknotter, hard unknots and unknotting number
This work addresses knot theory problems for mathematicians and computational researchers, but it is incremental as it applies existing reinforcement learning methods to a new domain.
The authors tackled the problem of simplifying knot diagrams using a reinforcement learning pipeline that learns move proposals and a value heuristic for Reidemeister moves, achieving recovery of the established upper bound of three for the unknotting number in a specific knot case.
We develop a reinforcement learning pipeline for simplifying knot diagrams. A trained agent learns move proposals and a value heuristic for navigating Reidemeister moves. The pipeline applies to arbitrary knots and links; we test it on ``very hard'' unknot diagrams and, using diagram inflation, on $4_1\#9_{10}$ where we recover the recently established and surprising upper bound of three for the unknotting number.